1. Field of the Invention
The present invention relates to a digital .SIGMA.-.DELTA. modulator applied to, e.g., an audio circuit, and used in an oversampling type D/A converter for sampling an input signal by a signal having a frequency much higher than the input signal to obtain a high S/N (signal-to-noise ratio).
2. Description of the Related Art
As is well known, in converting and coding an analog signal into a digital signal, when the analog signal is sampled at a frequency twice as high as a signal frequency band f.sub.B, the information of the original signal is not degraded in accordance with a Nyquist theorem. For this reason, a sampling frequency f.sub.S of a general D/A converter is set to about 2.2 to 2.4 times the signal frequency band f.sub.B. To the contrary, an oversampling type D/A converter in which the sampling frequency f.sub.S is set much higher than the signal frequency band f.sub.B to improve conversion precision is developed and put into practice.
A maximum S/N value S/N.sub.max of a simple oversampling type D/A converter is as given below if the number of bits (resolution) is defined as n: EQU S/N.sub.max =(3/2)2.sup.2n (f.sub.S /2f.sub.B)
Judging from the above equation, when the resolution of the D/A converter is increased by one bit, the S/N ratio is increased by 6 dB. However, even if the sampling frequency is doubled, the S/N ratio is apparently increased by only 3 dB.
Various techniques for increasing the S/N ratio without greatly increasing the sampling frequency f.sub.S have been developed. One of the examples is a D/A converter using .SIGMA.-.DELTA. modulation.
FIG. 15 shows a 1-bit D/A converter using a first-order .SIGMA.-.DELTA. modulator. Referring to FIG. 10, reference numeral X(z) denotes a digital input signal; Y(z), a digital output signal; and E(z), a quantization error. X(z), Y(z), E(z) denote a z-transform. The digital input signal X(z) is supplied to one input terminal of a subtracter 11. An output from the subtracter 11 is input to an adder 13 constituting an integrator 12. The integrator 12 is constituted by the adder 13 and a one-clock delay circuit 14 having a one-clock delay time. An output from the integrator 12 is supplied to a quantizer 15 and is quantized thereby. The output signal Y(z) from the quantizer 15 is supplied to a D/A converter 16 and to the other input terminal of the subtracter 11 through a one-clock delay circuit 17. The following equation is established in this circuit: EQU Y(z)=X(z)+(1-z.sup.-1)E(z)
The quantization error E(z) generally has no correlation with the input signal X(z) and is assumed to have flat frequency characteristics. For this reason, the noise frequency characteristics of this system are given by: EQU (1-e.sup.j.omega.T)=j.omega.T for .omega.T&lt;&lt;1
Where T is the period of the system clock signal. When the signal frequency band f.sub.B is set sufficiently lower than the sampling frequency f.sub.S, the noise is proportional to the frequency. Therefore, the S/N ratio can be increased by 9 dB in the signal band every time the sampling frequency f.sub.S is doubled.
FIG. 16 shows an nth-order .SIGMA.-.DELTA. modulator. In this nth-order .SIGMA.-.DELTA. modulator, subtracters 11 and integrators 12 are connected in series with each other in n stages. An output signal from a quantizer 15 is supplied to the other input terminal of each subtracter 11 through a one-clock delay circuit 17.
This nth-order .SIGMA.-.DELTA. modulator has transfer characteristics represented as follows: EQU Y(z)=X(z)+(1-z.sup.-1).sup.n E(z)
When this nth-order .SIGMA.-.DELTA. modulator is used in a D/A converter, the S/N ratio can be increased by 3.times.(2n+1) dB in the signal band every time the sampling frequency f.sub.S is doubled.
In this manner, the oversampling D/A converter using the .SIGMA.-.DELTA. modulator can increase the S/N ratio by increasing the sampling rate. For example, however, when a stereo signal is processed, D/A converters for two channels must generally be incorporated. For this reason, two .SIGMA.-.DELTA. modulators are required. When this circuit is to be formed into an IC, a large number of circuit elements are required to increase the cost.